Graph the following functions showing the x-intercepts and the vertex.
y=x^2-4
To graph the function y=x^2-4, we can start by finding the x-intercepts and the vertex.
To find the x-intercepts, we set y=0 and solve for x:
0 = x^2 - 4
x^2 = 4
By taking the square root of both sides, we have:
x = ±2
So, the x-intercepts are x = -2 and x = 2.
To find the vertex, we can use the formula x = -b/(2a), where a and b are the coefficients of the quadratic equation.
In this case, a = 1 and b = 0, so the equation becomes:
x = -(0)/(2*1)
x = 0
The y-coordinate of the vertex can be found by substituting the x-coordinate into the equation:
y = (0)^2 - 4
y = 0 - 4
y = -4
So, the vertex is at (0, -4).
Now we can plot the x-intercepts and the vertex on a graph:
-2 0 2
|_________________|__________________|
The x-intercepts are at x = -2 and x = 2.
The vertex is at (0, -4).
The graph of the function y=x^2-4 would be a parabola opening upwards and passing through these points.
To graph the function y = x^2 - 4, we need to find the x-intercepts and the vertex.
To find the x-intercepts, set y = 0 and solve for x:
0 = x^2 - 4
x^2 = 4
x = ±√4
x = ±2
So the x-intercepts are x = -2 and x = 2.
To find the vertex, we use the formula x = -b/(2a), where a and b are the coefficients of the quadratic function. In this case, a = 1 and b = 0.
x = -0/(2*1)
x = 0
To find the corresponding y-coordinate of the vertex, substitute x = 0 into the equation:
y = (0)^2 - 4
y = 0 - 4
y = -4
So the vertex is at (0, -4).
Now, let's plot the x-intercepts (-2, 0) and (2, 0), as well as the vertex (0, -4) on a graph:
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-4 --------------|--------------
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-3 -2 -1 0 1 2 3 4
The graph of the function y = x^2 - 4 will be a U-shaped parabola opening upwards, passing through the x-intercepts (-2, 0) and (2, 0), and its vertex will be at (0, -4).